What is the solution for (D^3+10D^2+25D)y=e^x ?

The solution for (D^3+10D^2+25D)y=e^x is y=c_{1}+c_{2}e^{-5x}+c_{3}xe^{-5x}+1/36 e^x

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(D^3+10D^2+25D)y=e^x

(D^{3} + 10 D^{2} + 25 D) y = e^{x}

y = c_{1} + c_{2} e^{- 5 x} + c_{3} x e^{- 5 x} + \frac{1}{36} e^{x}

Solution steps

(D^{3} + 10 D^{2} + 25 D) y = e^{x}

Solve linear ODE:

y = c_{1} + c_{2} e^{- 5 x} + c_{3} x e^{- 5 x} + \frac{1}{36} e^{x}

y = c_{1} + c_{2} e^{- 5 x} + c_{3} x e^{- 5 x} + \frac{1}{36} e^{x}

y^{^{'''}} - 3 y^{^{''}} + 2 y^{^{'}} = x + e^{x}

y^{^{''}} + 3 y^{^{'}} = 4

2 y^{^{''}} + y^{^{'}} - y = 3 x + 4, y (0) = 1, y^{^{'}} (0) = 1

y^{^{''}} + 9 y = 18 sin (3 t)

y^{^{''}} - y^{^{'}} - 6 y = 3 e^{2 x}

What is the solution for (D^3+10D^2+25D)y=e^x ?
The solution for (D^3+10D^2+25D)y=e^x is y=c_{1}+c_{2}e^{-5x}+c_{3}xe^{-5x}+1/36 e^x